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Question

The sum of three terms in A.P. is 15. If sum of their squares is 77 , find the three numbers.

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Solution

et a-d, a ,a+d are three terms in AP
sum of three terms = 15
a-d+a+a+d =15
⇒3a=15
a=15/3
a= 5--(1)
==============
sum of the squares of the extremes = 58
(a-d)²+(a+d)²= 58
⇒2(a²+d²) =58
⇒a²+d²=58/2
⇒5²+d²= 29 [ from (1)]
⇒d² = 29-25
∴d²=4
d= 2 or -2
===============
required three terms are
if a=5 , d= 2
a-d, a, a+d
(5-2),5,(5+2)
3,5,7
===============
if a=5 , d=-2
[5-(-2)], 5, [5+(-2)]
7,5,3

Read more on Brainly.in - https://brainly.in/question/1131942#readmore

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